As Dale notes in his reply to Jones, "Semantics and compositionality" it may all boil down to 'lambda'. As used in his PhD dissertation:
"λ(x) > 1."
As he notes, there are two functions involved in the compositional meaning-theory:
the lambda-function
λ(x) =df the number of characters in the string x.
the g function.
g(x,i) =df the ith character from the right of string x.
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More later, I hope.
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No, no, no! I am soooooo sorry. It is my fault. That definition at the beginning of Chapter 4 is not at all a compositional meaning theory (a CMT) in the sense required by a theory of meaning. I guess I am just really unclear in what I am trying to do at the beginning of Chapter 4. All that is is AN EXAMPLE of compositionality as it works when we map numerals onto numbers. That is all. That example, that definition with λ(x) and g(x, i) is about mapping numerals onto numbers, not about mapping sentences onto meanings.
ReplyDeleteI do say right before the example that I am giving a "compositional semantic theory" (not a "compositional meaning theory"). I say:
"Here's a more interesting example: a CST that entails for each Arabic-decimal numeral, a theorem that says which number is conventionally expressed by that numeral:"
I am talking about what I say here: mapping numerals onto numbers. That is all. It is an example. A sort of model to give the reader the sense of what such a mapping looks like.
Please, let me know if this is unclear. I suppose I should have written more to set this example up.
I hope that what I am saying here helps.
Yours,
Russell
Sure it does!
ReplyDeleteI actually think that distinction is a very fine one!
More later, I hope.